Armature windings and dynamo-electric machine using the same

ABSTRACT

An armature winding includes a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, and a main insulator for covering the strand group. A flow resistance of a current passing though the strands on an upper and a lower side in the cross-section of the strand group is set larger than a flow resistance of a current which passes through the strands in a central portion, or a flow resistance of a current passing through at least one of the plurality of strand groups is set larger than a flow resistance of a current passing through the remaining strand groups.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to armature windings and a dynamo-electric machine using the same, and more particularly, to armature windings suitable for exposure to a varying magnetic field, such as armature windings of a turbine generator, by way of example, and a dynamo-electric machine using the same.

2. Description of the Related Art

Armature windings for conventional turbine generators are described, for example, in U.S. Pat. No. 2,821,641. As illustrated in FIG. 17, in an example described in U.S. Pat. No. 2,821,641, a plurality of strands arranged in multiple tiers are transposed in the middle, and transpose angles of the strands are determined to be 360°, 540°, and the like, as shown in FIGS. 18A, 18B, depending on the power and mechanical dimensions of a particular type of machine for fitting in a slot, such that flux linkages are canceled out within the slot to reduce a loss caused by circulating currents which flow among strands. Specifically, as illustrated in FIG. 17, a strand 11 positioned at the topmost tier of the right row is transposed to the topmost tier of the left row, i.e., on a strand 1 (2 n), and right-hand strands 12, 13 positioned at the topmost tier of the right row are sequentially transposed to make the overall winding in a stranded structure. Also, the transpose angle used herein is a 360° transposition in which strands 11, 15 wound from a shaft end I are transposed, and make a round to return to the same positions at a shaft end II, or a 540° transposition in which the strands are transposed further by an extra half cycle. In this event, the angle such as 360° and 54020 , and the pitch of transposition are selected such that magnetic fields interlining between windings are canceled out within a fixed iron core 30. For example, the angle and pitch are selected such that a total of magnetic flux φ31 and φ33 interlining between strands 11 and 15 are equal to a magnetic flux φ32 which interlinks in a reverse direction.

JP-A-47-12513 also describes armature windings for a turbine generator. As illustrated in FIG. 19, in this example, two rows of strand group 2 are disposed outside of a strand group 1 transposed over two rows, and strands 21, 22, 23 and the like are interposed to surround the strand group 1. This is intended to reduce a circulating current loss caused by a radial flux φr2.

In U.S. Pat. No. 2,821,641, even though strands are transposed in a strand group, a magnetic flux φ1 interlining at the end I and a magnetic flux φ2 interlining at the end II have the same polarity as each other through a transposition of 360°, so that a magnetic flux (φ1+φ2) interlinks within a closed loop defined by strands 11, 15, and the like. With a transposition of 540°, on the other hand, the magnetic flux φ1 interlinking at the end I of the strands 1, 15 and the magnetic flux φ2 interlining at the end II have the polarities which cancel each other, but the magnetic fields φ1, φ2 are not equal in magnitude because the strands are different in radial position at the end I and end II. In other words, the flux linkage, corresponding to the difference (φ1−100 2) in field strength, remains, thus making it difficult to thoroughly cancel out circulating currents which flow around the strands 11, 15. Thus, there exists not a few current component which circulates among strands.

When a cross-sectional area of strands must be ensured, a winding as shown in FIG. 20 has been used, in which a plurality of transposed strand groups are arranged in parallel. Since such a structure cannot at all cancel out a radial magnetic flux φr2 which interlinks between the strand group 1 and strand group 2, even an increased currents circulate among the strands.

On the other hand, JP-A-47-12513, which is a technique for reducing the radial magnetic flux, involves a complicated structure in which the strand group 2 is arranged in a double configuration to surround the strand group 1, as illustrated in FIG. 19, requiring a large number of manufacturing steps. Also, for example, the strand 11 must be transposed onto a strand 1 (2 n), and a strand 21 is further transposed on the step, thus making it difficult to maintain a uniform gap between strands. For this reason, an appropriate insulating strength cannot be maintained.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide armature windings which solve the problems mentioned above, and a dynamo-electric machine using the same.

To achieve the above object, the present invention provides an armature winding which comprises a strand group having strands transposed and bound in at least two rows and multiple tiers, and a main insulator for covering the strand group, wherein a flow resistance of a current passing though the strands on an upper and a lower side in the cross-section of the strand group is set larger than a flow resistance of a current which passes through the strands in a central portion.

The present invention also provides an armature winding which comprises a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, and a main insulator for covering the plurality of strand groups, wherein a flow resistance of a current passing though at least one of the plurality of strand groups is set larger than a flow resistance of a current which passes through the remaining strand groups.

According to the present invention, it is possible to reduce a circulating current within the armature winding of a dynamo-electric motor to uniformalize the temperature.

Other objects, features and advantages of the invention will become apparent from the following description of the embodiments of the invention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a general view illustrating an outline of a turbine generator which employs armature windings of the present invention;

FIG. 2 is a cross-sectional view illustrating an armature winding according to a first embodiment of the present invention;

FIG. 3 is a cross-sectional view illustrating an armature winding according to a second embodiment of the present invention;

FIG. 4 is a cross-sectional view illustrating an armature winding according to a third embodiment of the present invention, when they are contained in a slot;

FIG. 5 is a cross-sectional view illustrating an armature winding according to a fourth embodiment of the present invention, when they are contained in a slot;

FIG. 6 is a cross-sectional view illustrating an armature winding according to a fifth embodiment of the present invention;

FIG. 7 is a cross-sectional view illustrating an armature winding according to a sixth embodiment of the present invention;

FIG. 8 is a cross-sectional view illustrating an armature winding according to a seventh embodiment of the present invention;

FIG. 9 is a cross-sectional view illustrating an armature winding according to an eighth embodiment of the present invention;

FIG. 10 is a cross-sectional view illustrating an armature winding according to a ninth embodiment of the present invention;

FIG. 11 is a diagram illustrating a conception of the whole length of armature windings using four rows of strands for explaining the relationship among a strand group, strands and flux linkage;

FIG. 12 is a diagram showing a relationship between the flux linkage and circulating current in FIG. 11;

FIGS. 13A, 13B are a current distribution graph of a conventional two-row winding and a cross-sectional view in this structure;

FIGS. 14A, 14B are a current distribution graph of a conventional four-row winding and a cross-sectional view in this structure;

FIGS. 15A, 15B are a current distribution graph in this structure and a cross-sectional view of the winding according to the second embodiment of the present invention;

FIG. 16 is a cross-sectional view illustrating an example of a conventional armature winding;

FIG. 17 is a partial perspective view illustrating how strands are transposed in a conventional two-row winding;

FIGS. 18A, 18B are conceptual diagrams illustrating how strands are arranged in a 540° transposition and in a 360° transposition, respectively;

FIG. 19 is a partial perspective view illustrating how strands are transposed in JP-A-47-12513; and

FIG. 20 is a partial perspective view illustrating how strands are transposed in a conventional four-row winding.

DETAILED DESCRIPTION OF THE EMBODIMENTS

For describing some embodiments of the present invention, the structure of a turbine generator, to which the present invention is applied, will be generally described with reference to FIG. 1. The basic structure illustrated in FIG. 1 does not depend on the type of cooling fluid.

As illustrated in FIG. 1, a rotor 51 is rotatably supported by a rotating shaft 50 to a stator frame 60. The rotor 51 internally has field windings (not shown), and serves as a magnetic pole. A stator core 30 forms part of a stator assembly which is disposed opposite to the rotor 51 through a predetermined gap. The stator core 30 has both axial ends held by end cramps 31, and fixed to the stator frame 60. Armature windings 10, 20 are stored in each of a plurality of slots which extend in the axial direction of the stator core 30, and are disposed in the circumferential direction at predetermined intervals. For a water cooling generator, a cooling water inlet passage 61 is provided at axial ends of the armature windings 10, 20, while a cooling water outlet passage 62 is provided on the opposite ends of the same, such that cooling water is passed in the axial direction through the hollow strands 11, 14 and the like, as illustrated in FIG. 3, which form part of the armature windings 10, 20, to directly cool the armature windings 10, 20.

Generally, the armature windings 10, 20 each have a group of strands arranged, for example, in n rows and m columns, which is covered with a main insulator 4. The main insulator 4 is a structure for maintaining electric insulation between the inside and the outside of the winding, and is often made of mica or resin. FIG. 2 illustrates an example of the armature winding 10 or 20 comprised of four columns (m=4) and two rows (n=23) in cross-section taken along a direction perpendicular to the axis, wherein strands 1 are numbered 11, 12, . . . , 1 n from the first row to the n-th row, where m, n are both arbitrary integers. Generally, strands are transposed every two rows to form a strand group. Likewise, in a four-column armature winding, strands are divided into groups 1, 2 of strands which are transposed every two row, as illustrated in FIG. 20. The same is applied as well to six columns or more.

[First Embodiment]

FIG. 2 illustrates an armature winding according to a first embodiment of the present invention. In the first embodiment, in the turbine generator illustrated in FIG. 1, a strand group 2, which forms part of the armature winding 10 covered with the main insulator, includes strands 21, 22, 2 n, the cross-sectional area of which is chosen to be smaller than the cross-sectional area of strands 11, 12, . . . , 1 n of a strand group 1, whereby the strand group 2 has a larger flow resistance of current than the strand group 1. The effects and principles of the foregoing will be discussed below.

As illustrated in FIG. 16, a general armature winding is comprised of a strand group 1 made up of two rows of strands 11, 12, . . . , 1 n, 1(n+1), . . . , 1(2 n), and a strand group 2 likewise made up of two rows of strands 21, 22, . . . , 2 n, 2(n+1), . . . , 2(2 n). The strand group 1 has the same cross-sectional shape as the second strand group 2. Here, the strands in the strand group 1 and strand group 2 are transposed through a transpose angle of 360°, 540° or the like, respectively, so as to cancel out magnetic fields which interlink within the stator core 30. The manner in which the strands are transposed has been shown in FIG. 20.

The relationship among the strand groups, strands, and flux linkage will be described with reference to FIGS. 11, 12. Within a stator core, strands are transposed two rows by two rows, as illustrated in FIG. 20, however, no strands are transposed between the strand group 1 and strand group 2, so that a radial magnetic flux φr2 acts between the strand groups. Also, the strands are transposed only within the stator core, and are not transposed in end portions. Both strand groups are connected to each other at extreme ends. Here, representative strands 11, 15, 21, 25 are selected from the respective strand groups for the following description. The transpose angle is chosen to be 540° by way of example. As illustrated in FIGS. 11, 18A, 18B, strands belonging to the strand group 1 are transposed such that the flux linkage is annihilated within a slot, so that no circulating current is induced between the strands 11, 15 by magnetic fields such as φr2, φt2 and the like. On the other hand, regarding magnetic fields around the end I and end II, since the strands 11, 15 change places in vertical relationship, a circumferential magnetic flux φt1 at the end I and a circumferential magnetic flux φt3 at the end II act on the strands 11, 15 in opposite polarities. However, since the magnetic fields vary depending on radial positions, the flux linkages are not completely canceled out, but a slight circulating current flows. This applies to the strands 21, 25 of the strand group 2 as well.

Next, description will be made on the influence of a magnetic flux which links between the strand group 1 and strand group 2. These two strand groups are not transposed to each other, and a total of the radial flux linkage φr1 within the slot and the radial magnetic fluxes φr2, φr3 at the ends links between the two strand groups. FIG. 12 illustrates a circuit diagram of strand currents, where a current I₀ is calculated by dividing a current I of the overall armature winding by the number of strands, and represents an average current of the strands, and I₁ to I₃ represent circulating currents which are generated by magnetic fluxes that link to respective closed loops. The circumferential magnetic fluxes φt1−φt3 link between the strands 11 and 15 and between the strands 21 and 25, respectively, to induce the circulating currents I1, I2 which flow in a direction in which they cancel out the magnetic fluxes. On the other hand, the radial magnetic fluxes φr1 to φr3 link between the strand group 1 and strand group 2, i.e., between the strands 11, 15 and between strands 21, 25 to induce the current I3 which flows in a direction in which it cancels out the magnetic fluxes. Stated another way, currents which flow through the strands 11, 15, 21, 25 are calculated as follows: I ₁₁ =I ₀ +I ₁ +I ₃ I ₁₅ =I ₀ −I ₁ +I ₃ I ₂₁ =I ₀ +I ₂ −I ₃ I ₂₅ =I ₀ −I ₂ −I ₃   (1)

The currents which flow through the respective strands are in a relationship given by: I ₁₁ >I ₁₅ >I ₂₁ >I ₂₅   (2)

It is understood from the above that the current values are different from one another on the respective strands.

In this event, a strand current distribution in the conventional structure may be represented by FIGS. 14A, 14B. The strand group 1, through which a large strand current flows, generates larger heat, while the strand group 2 generates smaller heat. Here, in 540° transposition, larger heat is generated in an upper and a lower portion of the winding from the relation between the positions of strands and the linkage flux at the ends. For this reason, a current distribution is produced as illustrated in FIG. 13 even when there is only one strand group, resulting in non-uniform temperature. On the other hand, in the first embodiment, the strand group 2 has a smaller flow resistance of current than the strand group 1. Thus, as a closed loop which circulates the strand groups 1, 2 has a larger resistance, the circulating current I₃ can be reduced. The smaller I₃ can contribute to a reduction in I₁₁, I₁₅, as shown by Equation (1), resulting in a reduction in heat generated by the strand group 1. In regard to the strand group 2, the current is reduced as the resistance is increased, however, heat generated thereby tends to increase because the flow resistance of current is larger. In other words, as illustrated in FIG. 15A, the temperature within the cross-section can be maintained uniform by an increase in the heat generated by the strand group 2 and a reduction in the heat generated by the strand group 1.

While the foregoing embodiment has been described in connection with an example in which the strand group 2 has a larger flow resistance of current than the stand group 1, similar effects can be produced when the strand group 1 has a smaller flow resistance of current than the strand group 2. In the foregoing embodiment, the flow resistance of current is increased by uniformly reducing the width of all the strands within the strand group 2, but the present invention is not limited to this particular way. Instead, the flow resistance of current may be varied, for example, by changing the material, or by changing the height of the strands, the shape of the strands, and the number of tiers, as a matter of course.

[Second Embodiment]

FIG. 3 illustrates an armature winding according to a second embodiment of the present invention. The second embodiment illustrates an application to a water-cooled winding. The flow resistance of current is varied by uniformly reducing the width of all the strands (cross-sectional area of the strands) within the strand group 2 than the width of the strands (cross-sectional area of the strands) within the strand group 1. By reducing the cross-sectional area of the strands within the strand group 2 than the cross-sectional area of the strands within the stand group 1, a closed loop formed by the strand 11 and the like within the strand group 1 and the strand 21 and the like within the strand group 2 has a larger flow resistance of current, so that a circulating current which flows through the closed loop can be reduced. Also, by reducing the cross-sectional area of the strands within the strand group 2, through which a smaller current flows, the current density of the strand group 1 can be made equivalent to that of the strand group 2, resulting in uniform heat generation as well. In the second embodiment which is applied to a water-cooled winding, the strands 11, 14, 21, 24, and the like are in hollow structure for passing cooling water therethrough, where the strands 21, 24 and the like have a smaller water pass area than the strands 11, 14, making it possible to further uniformalize the temperature because an appropriate amount of water can be taken in accordance with generated heat.

[Third Embodiment]

FIG. 4 illustrates an armature winding according to a third embodiment of the present invention. The third embodiment shows an example which has armature windings 10, 20 (hereinafter called the “top coil 20” and “bottom coil 10”), in the structure described in the second embodiment, piled two high within a slot 40. In this embodiment, the width of strands 121, 122, and the like (cross-sectional area of the strands) belonging to a strand group 102 of the bottom coil 10 is set smaller than the width of strands 111, 112, and the like (cross-sectional area of the strands) belonging to a strand group 101. In the top coil 20, the width of strands 221, 222, and the like (cross-sectional area of the strands) belonging to a strand group 202 is set smaller than the width of strands 211, 212, and the like of a strand group 201. In other words, the strands having a larger resistance are placed on the same side in regard to the horizontal direction of the slot in both the top coil 20 and bottom coil 10. This is effective when a current flowing through the top coil 20 has the same polarity as a current flowing through the bottom coil 10 so that radial magnetic fluxes having the same polarity act on the coils.

[Fourth Embodiment]

FIG. 5 illustrates an armature winding according to a fourth embodiment of the present invention. The fourth embodiment shows an example which has armature windings 110, 220 (hereinafter called the “top coil 220” and “bottom coil 110”) placed in a slot 40, in which the structure described in the first embodiment is applied to a water-cooled windings. In this embodiment, the width of strands 121, 122, and the like (cross-sectional area of the strands) belonging to a strand group 102 of the bottom coil 110 is smaller than the width of the strands 111, 112, and the like (cross-sectional area of the strands) belonging to a strand group 101. In the top coil 220, the width of strands 211, 212, and the like (cross-sectional area of the strands) belonging to a strand group 201 is smaller than the width of strands 221, 222, and the like belonging to a strand group 202. In other words, the strands having a larger resistance are placed on the opposite sides in regard to the horizontal direction of the slot 40 in the top coil 220 and bottom coil 110. This structure is effective when a current flowing through the top coil 220 is opposite in polarity to a current flowing through the bottom coil 110, and radial magnetic fluxes acting on the top coil 220 and bottom coil 110 have the same polarity, or when a current flowing through the top coil 220 has the same polarity as a current flowing through the bottom coil 110, and acting radial magnetic fluxes have the opposite polarities.

[Fifth Embodiment]

FIG. 6 illustrates an armature winding according to a fifth embodiment of the present invention. In the embodiment illustrated in FIG. 6, hollow strands 21, 24, and the like are placed only in an upper portion and a lower portion of a strand group 2, while a strand group 1 is similar in structure to the second embodiment (see FIG. 3). In the structure of such an embodiment, a smaller amount of cooling water can be provided to the strand group 2 which generates a reduced amount of heat, so that effective cooling can be accomplished as appropriate to a particular amount of generated heat. Also, since larger heat is generated in the upper portion and lower portion of the strand group 2, as illustrated in FIGS. 14A, 14B, these portions can be intensively cooled in the structure of this embodiment, thereby improving the cooling efficiency.

[Sixth Embodiment]

FIG. 7 illustrates an armature winding according to a sixth embodiment of the present invention. This embodiment shows an exemplary application to an armature winding which uses 6-row strands, and comprises three strand groups 1, 2, 3. In this example, the width of strands (cross-sectional area of the strands) belonging to the strand group 2 is smaller than the width of strands (cross-sectional area of the strands) belonging to the first strand group 1, and the width of strands (cross-sectional area of the strands) belonging to the strand group 3 is smaller than the width of the strands (cross-sectional area of the strands) belonging to the strand group 2. In this way, even when the number of strand groups is increased, similar effects can be produced as in the second embodiment which is comprised of two strand groups by increasing or decreasing the cross-sectional area of the strands in accordance with circulating currents which flow through the respective strands.

[Seventh Embodiment]

FIG. 8 illustrates an armature winding according to an eighth embodiment of the present invention. This embodiment shows an exemplary application to an armature winding comprised of a single strand group, and illustrates an exemplary arrangement of strands at an end. In a general two-row coil, the heat generation density is higher in an upper portion and a lower portion of a winding due to the influence of circulating currents, as illustrated in FIGS. 13A, 13B. To solve this problem, in this embodiment, the cross-sectional area of strands 11, 12, and the like in an upper portion and a strand in and the like in a lower portion, in which a larger amount of heat is generated, is smaller than the cross-sectional area of the remaining (central) strands. In other words, the flow resistances of currents passing through the strands in the upper and lower portions are set larger than the flow resistances of currents passing through central strands. By thus reducing the cross-sectional area of the strands in the upper and lower portions, it is possible to reduce an additional loss, for example, an eddy current loss produced in these portions and uniformalize the temperature.

[Eighth Embodiment]

FIG. 9 illustrates an armature winding according to an eighth embodiment of the present invention. This embodiment shows an exemplary application to an armature winding comprised of a single strand group, wherein hollow strands 11, 14, and the like for water cooling are intensively arranged in an upper portion and a lower portion, in which the heat generation density is higher, to more strongly cool the upper and lower portions of the winding. In the structure of this embodiment, the upper and lower portions of the winding, in which a larger amount of heat is generated, can be cooled in an intensive way to improve the cooling efficiency and uniformalize the temperature.

[Ninth Embodiment]

FIG. 10 illustrates an armature winding according to a ninth embodiment of the present invention. This embodiment, which is created from a viewpoint different from the eighth embodiment, intensively arranges hollow strands 11, 12, and the like only in an upper portion of a winding. With a strand transposition through 360°, the circulating current typically becomes largest on the upper side of armature windings 10, 20, so that this embodiment can intensively cool this portion to uniformalize the temperature.

According to the present invention, the circulating currents within the winding are reduced to eliminate locally heated portions, thereby making it possible to uniformly increase the temperature of the armature and reduce the increase in temperature.

It should be further understood by those skilled in the art that although the foregoing description has been made on embodiments of the invention, the invention is not limited thereto and various changes and modifications may be made without departing from the spirit of the invention and the scope of the appended claims. 

1. An armature winding comprising: a strand group having strands transposed and bound in at least two rows and multiple tiers; and a main insulator for covering said strand group, wherein a flow resistance of a current passing though said strands on an upper and a lower side in the cross-section of said strand group is set larger than a flow resistance of a current which passes through said strands in a central portion.
 2. An armature winding comprising: a strand group having strands transposed and bound in at least two rows and multiple tiers; and a main insulator for covering said strand group, wherein said strands on an upper and a lower side in the cross-section of said strand group are formed to have a smaller cross-sectional area than a cross-sectional area of said strands in a central portion.
 3. An armature winding comprising: a strand group having strands stranded and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said strand group, wherein said hollow strands are intensively arranged on an upper and a lower side in the cross-section of said strand group, and said solid strands are intensively arranged in a central portion.
 4. An armature winding comprising: a strand group having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said strand group, wherein said hollow strands are intensively arranged only on an upper side in the cross-section of said strand group, and said solid strands are arranged in the remaining area.
 5. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers; and a main insulator for covering said plurality of strand groups, wherein a flow resistance of a current passing though at least one of said plurality of strand groups is set larger than a flow resistance of a current which passes through the remaining strand groups.
 6. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers; and a main insulator for covering said plurality of strand groups, wherein a cross-sectional area of strands belonging to at least one strand group in the cross-section of said plurality of strand groups is smaller than a cross-sectional area of strands belonging to the remaining strand groups.
 7. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said plurality of strand groups, wherein a flow resistance of a current passing through at least one strand group of said plurality of strand groups is set larger than a flow resistance of a current passing through the remaining strand groups.
 8. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said plurality of strand groups, wherein a cross-sectional area of strands belonging to at least one strand group in the cross-section of said plurality of strand groups is smaller than a cross-sectional area of strands belonging to the remaining strand groups.
 9. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said plurality of strand groups, wherein the hollow strands in at least one of said plurality of strand groups have a water pass area smaller than a water pass area of the hollow strands in the remaining strand groups.
 10. An armature winding comprising: a plurality of strand groups each having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said plurality of strand groups, wherein said hollow strands are arranged on an upper side and a lower side in the cross-section of at least one of said plurality of strand groups, said solid strands are arranged in a central portion, and said solid strands and said hollow strands are mixed in the remaining strand groups.
 11. An armature winding comprising: three strand groups each having strands transposed and bound in at least two rows and multiple tiers, said strands including solid strands and hollow strands through which a cooling medium passes; and a main insulator for covering said three strand groups, wherein said strands belonging to a strand group positioned on one side of a strand group positioned at the center of said three strand groups have a cross-sectional area smaller than a cross-sectional area of said strands belonging to said central strand group, and said strand belonging to a strand group positioned on the other side of said central strand group has a cross-sectional area larger than the cross-sectional area of said strands belong to said central strand group.
 12. A dynamo-electric machine comprising: a rotor core; a rotor including a field winding stored in a slot of said rotor core; and a stator disposed opposite to said rotor with a predetermined gap therebetween, and including a stator core, and an armature winding according to any of claims 1 to 11 stored in a slot of said stator core.
 13. A dynamo-electric machine comprising: a rotor core; a rotor including a field winding stored in a slot of said rotor core; and a stator disposed opposite to said rotor with a predetermined gap therebetween, and including a stator core, and armature windings stored in a slot of said stator core, said armature windings including a bottom coil and a top coil stored in the slot of said stator core, said bottom coil and said top coil comprising armature windings according to any of claims 7 to
 9. 14. A dynamo-electric machine comprising: a rotor core; a rotor including a field winding stored in a slot of said rotor core; and a stator disposed opposite to said rotor with a predetermined gap therebetween, and including a stator core, and an armature winding stored in a slot of said stator core, said armature winding including a bottom coil and a top coil stored in the slot of said stator core, said bottom coil comprising an armature winding according to any of claims 7 to 9, said top coil comprising an armature winding which has strand groups disposed opposite to the strand groups of said bottom coil. 